Case Studies in Science Education: Erien Erien strives to include and manage class discussions in science learning and wants to increase her students' higher-level thinking skills.,The segment shows the teacher giving an assignment to the class to design a building near the wetlands and a stream. They are given specific roles to represent as part of the planning process and they must defend their positions. They then make a presentation to the town meeting to discuss the pros and cons of the building development.Author(s): Harvard-Smithsonian Center for Astrophysics

Looking at Learning...Again, Part 1: Workshop 8. The International Picture This workshop offers an opportunity to investigate various aspects of the Third International Mathematics and Science Study (TIMSS), other than the test scores themselves. Distinguished Professor of Educational Psychology William Schmidt presents differences in curricula, textbooks, and teaching practices around the world, and a group of community members discuss how the TIMSS results reflect societal and cultural values.,Professional development activity for viewers to think about, write down aAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,How a Mathematician Approaches Problems - Fern Hunt, a mathematician at the National Institute for Standards and Technology, is seen as she collaborates with colleagues to solve difficult technical problems. Using the metaphor of the childrens game Towers of Hanoi, she explains her approach to solving problems. 15 mAuthor(s): Harvard-Smithsonian Center for Astrophysics

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Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teachers role in fostering thoughtful mathematics.,Equations In Colts Neck, New Jersey, fourth-grade teacher and former Rutgers researcher Amy Martino finds out that what started as a 15-minute warm-up question evolves into an interesting discussion about equations.Author(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teachers role in fostering thoughtful mathematics.,Englewood, NJ  Fourth Grade: Towers Fourth-grade teacher Blanche Young attempts the Towers activity for the first time with her students. She feels that their work is valuable, but questions how much time these open-ended activities are taking away from the standard curriculAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teachers role in fostering thoughtful mathematics.,Englewood, NJ  Fourth Grade: Towers Fourth-grade teacher Blanche Young attempts the Towers activity for the first time with her students. She feels that their work is valuable, but questions how much time these open-ended activities are taking away from the standard curriculAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teachers role in fostering thoughtful mathematics.,Englewood, NJ  Fourth Grade: Towers Fourth-grade teacher Blanche Young attempts the Towers activity for the first time with her students. She feels that their work is valuable, but questions how much time these open-ended activities are taking away from the standard curriculAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teachers role in fostering thoughtful mathematics.,EnglewoodKindergarten: Stacking Blocks In Englewood, New Jersey, a kindergarten teacher uses blocks as mathematical objects in an addition activity.Author(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 5. Building on Useful Ideas One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is on the teachers role in fostering thoughtful mathematics.,EnglewoodKindergarten: Stacking Blocks In Englewood, New Jersey, a kindergarten teacher uses blocks as mathematical objects in an addition activity.Author(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,Revisiting Problems After Five Years - Kenilworth 10th graders reexamine the same problem they had last seen in the fifth gradethe Pizza problem. One student, Michael, uses the binary number system to his advantage.Author(s): Harvard-Smithsonian Center for Astrophysics

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Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,How a Mathematician Approaches Problems - Fern Hunt, a mathematician at the National Institute for Standards and Technology, is seen as she collaborates with colleagues to solve difficult technical problems. Using the metaphor of the childrens game Towers of Hanoi, she explains her approach to solving problems. 15 mAuthor(s): Harvard-Smithsonian Center for Astrophysics

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Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,How a Mathematician Approaches Problems - Fern Hunt, a mathematician at the National Institute for Standards and Technology, is seen as she collaborates with colleagues to solve difficult technical problems. Using the metaphor of the childrens game Towers of Hanoi, she explains her approach to solving problems. 15 Author(s): Harvard-Smithsonian Center for Astrophysics

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Private Universe Project in Mathematics: Workshop 3. Inventing Notations We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New JerseyAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 3. Inventing Notations We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New JerseyAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 3. Inventing Notations We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New JerseyAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 3. Inventing Notations We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New JerseyAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 2. Are You Convinced? Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to giveAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 3. Inventing Notations We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,Kenilworth Study: Pizzas In the fourth grade, the students encounter counting problems where the solutions cannot be built using standard manipulatives. As he invents his own notation systems, one student, Matt, builds on previous work to arrive at a solution Author(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 2. Are You Convinced? Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to giveAuthor(s): Harvard-Smithsonian Center for Astrophysics

Private Universe Project in Mathematics: Workshop 2. Are You Convinced? Proof making is one of the key ideas in mathematics. Looking at teachers and students grappling with the same probability problem, we see how two kinds of proofproof by cases and proof by inductionnaturally grow out of the need to justify and convince others.,Englewood, New JerseyTeachers Workshop Englewood, a town with unsatisfactory student test scores, is implementing a long-term project to improve math achievement. As part of a professional development workshop designed in part to giveAuthor(s): Harvard-Smithsonian Center for Astrophysics